You can sponsor your husband but will need a joint sponsor who is a permanent residfent or citizen who earns sufficient income to sponsor him. They will not be responsible for you and your kids by being a joint sponsor for your husband.
Go to "www.USCIS.gov" Look for the "FORMS" tab at the top left of the page and click it. Scroll down the form "I-864P" This will show you how much income is required for the sponsor. You will be required to file a form I-864 but if your income is not sufficient you will also need a co-sponsor. The co-sponsor does not need to be a family member - any U.S. Citizen or Lawful Permanent Resident can file the I-864 on your spouse's behalf. As for liability - the co-sponsor is only liable for the intending immigrant. The sponsor will remain liable for any Cash payments from the government (this does not include emergency medical) until one of the following occurs: 1. The immigrant has earned 40 quarters in the Social Security system, 2. He leaves the U.S. permanently, 3. He becomes a U.S. Citizen, or 4. He he Dies. Please note - Divorce does not sever the sponsor's liability. You should consult with an immigration attorney before filing any forms with the government.